`int_(0)^(1)(x e^(x)+sin.(pix)/(4))dx`

Explanation

`int_(0)^(1)(xe^x)+sin.(pi.x)/(4))dx`
`=int_(0)^(1)xe^(x)dx+int_(0)^(1)sin((pi.x)/(4))dx`
`=[xe^(x)-int1.e^(x)dx]_(0)^(1)+[(-cos.(pi.x)/(4))/((pi)/(4))]_(0)^(1)`
`=[xe^(x)-e^(x)]_(0)^(1)-(4)/(pi)[cos((pi.x)/(4))]_(0)^(1)`
`=(e-e)-(0-e^(0))-(4)/(pi)(cos.(pi)/(4)-cos 0)`
`=0-(-1)-(4)/(pi)((1)/(sqrt2)-1)`
`=1-(4)/(pi)((1-sqrt2)/(sqrt2))xx(sqrt2)/(sqrt2)`
`=1+(2)/(pi)(2-sqrt2)=1+(4)/(pi)-(2sqrt2)/(pi)`